Question : The ratio of three positive numbers is 2 : 3 : 5 and the sum of their squares is 608. The three numbers are:
Option 1: 2, 3 and 5
Option 2: 10, 15 and 25
Option 3: 8, 12 and 20
Option 4: 4, 6 and 10
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Correct Answer: 8, 12 and 20
Solution : Given: The ratio of three positive numbers is 2 : 3 : 5. The sum of their squares is 608. Let the number be $2x, 3x$ and $5x$. As per the given conditions, $(2x)^{2}+(3x)^{2}+(5x)^{2}=608$ ⇒ $4x^{2}+9x^{2}+25x^{2}=608$ ⇒ $38x^{2}=608$ ⇒ $x^{2}=\frac{608}{38}=16$ ⇒ $x^{2}=16$ ⇒ $x=4$ So, the positive numbers are 8, 12 and 20. Hence, the correct answer is 8, 12 and 20.
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